Use the Rational Roots Test to Find All Possible Roots f(x)=33x^4+28x^3+48x^2+140x+45

$f (x) = 33 x^{4} + 28 x^{3} + 48 x^{2} + 140 x + 45$

Step 1

If a polynomial function has integer coefficients, then every rational zero will have the form $\frac{p}{q}$ where $p$ is a factor of the constant and $q$ is a factor of the leading coefficient.

$p = \pm 1, \pm 3, \pm 5, \pm 9, \pm 15, \pm 45$

$q = \pm 1, \pm 3, \pm 11, \pm 33$

Step 2

Find every combination of $\pm \frac{p}{q}$ . These are the possible roots of the polynomial function.

$\pm 1, \pm \frac{1}{3}, \pm \frac{1}{11}, \pm \frac{1}{33}, \pm 3, \pm \frac{3}{11}, \pm 5, \pm \frac{5}{3}, \pm \frac{5}{11}, \pm \frac{5}{33}, \pm 9, \pm \frac{9}{11}, \pm 15, \pm \frac{15}{11}, \pm 45, \pm \frac{45}{11}$

Use the Rational Roots Test to Find All Possible Roots f(x)=33x^4+28x^3+48x^2+140x+45

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